Advertisements
Advertisements
प्रश्न
Which of the following is irrational?
विकल्प
`sqrt(4/9)`
`sqrt(12)/sqrt(3)`
`sqrt(7)`
`sqrt(81)`
उत्तर
`bb(sqrt(7))`
Explanation:
Irrational numbers are real numbers which cannot be represented as simple fractions.
Examples: `sqrt(2), sqrt(3), pi`
`sqrt(4/9) = 2/3` ...(Rational)
`sqrt(12)/sqrt(3) = (2sqrt(3))/sqrt(3) = 2` ...(Rational)
`sqrt(81) = 9` ...(Rational)
But `sqrt(7)` is an irrational number.
APPEARS IN
संबंधित प्रश्न
Examine, whether the following number are rational or irrational:
`sqrt3+sqrt2`
Examine, whether the following number are rational or irrational:
`(sqrt2-2)^2`
Prove that `1/sqrt (3)` is irrational.
An irrational number between 2 and 2.5 is
State whether the following statement is true or false. Justify your answer.
Every point on the number line is of the form `sqrt m`, where m is a natural number.
State, whether the following numbers is rational or not:
(√3 - √2)2
Insert a rational number and an irrational number between the following:
2.357 and 3.121
Show that x is irrational, if x2 = 6.
Prove that `7 + 4sqrt(5)` is an irrational number, given that `sqrt(5)` is an irrational number.
Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1 P2 perpendicular to OP1 of unit length. Now draw a line segment P2 P3 perpendicular to OP2. Then draw a line segment P3 P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn–1Pn by drawing a line segment of unit length perpendicular to OPn–1. In this manner, you will have created the points P2, P3,...., Pn,.... ., and joined them to create a beautiful spiral depicting `sqrt2, sqrt3, sqrt4,` ...